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CONTENTS
1 THERMAL RADIATION AND PLANCK'S POSTULATE 1
1-1 Introduction 2
1-2 Thermal Radiation 2
1-3 Classical Theory of Cavity Radiation 6
1-4 Planck's Theory of Cavity Radiation 13
1-5 The Use of Planck's Radiation Law in Thermometry 19
1-6 Planck's Postulate and Its Implications 20
1-7 A Bit of Quantum History 21
2 PHOTONS—PARTICLELIKE PROPERTIES OF RADIATION 26
2-1 Introduction 27
2-2 The Photoelectric Effect 27
2-3 Einstein's Quantum Theory of the Photoelectric Effect 29
2-4 The Compton Effect 34
2-5 The Dual Nature of Electromagnetic Radiation 40
2-6 Photons and X-Ray Production 40
2-7 Pair Production and Pair Annihilation 43
2-8 Cross Sections for Photon Absorption and Scattering 48
3 DE BROGLIE'S POSTULATE—WAVELIKE PROPERTIES
OF PARTICLES 55
3-1 Matter Waves 56
3-2 The Wave-Particle Duality 62
3-3 The Uncertainty Principle 65
3-4 Properties of Matter Waves 69
3-5 Some Consequences of the Uncertainty Principle 77
3-6 The Philosophy of Quantum Theory 79
4 BOHR'S MODEL OF THE ATOM 85
4-1 Thomson's Model 86
4-2 Rutherford's Model 90
4-3 The Stability of the Nuclear Atom 95
4-4 Atomic Spectra 96
4-5 Bohr's Postulates 98
4-6 Bohr's Model 100
4-7 Correction for Finite Nuclear Mass 105
4-8 Atomic Energy States 107
4-9 Interpretation of the Quantization Rules 110
4-10 Sommerfeld's Model 114
4-11 The Correspondence Principle 117
4-12 A Critique of the Old Quantum Theory 118
ix CONTENTS
5 SCHROEDINGER'S THEORY OF QUANTUM MECHANICS 124
5-1 Introduction 125
5-2 Plausibility Argument Leading to Schroedinger's Equation 128
5-3 Born's Interpretation of Wave Functions 134
5-4 Expectation Values 141
5-5 The Time-Independent Schroedinger Equation 150
5-6 Required Properties of Eigenfunctions 155
5-7 Energy Quantization in the Schroedinger Theory 157
5-8 Summary 165
6 SOLUTIONS OF TIME-INDEPENDENT
SCHROEDINGER EQUATIONS 176
6-1 Introduction 177
6-2 The Zero Potential 178
6-3 The Step Potential (Energy Less Than Step Height) 184
6-4 The Step Potential (Energy Greater Than Step Height) 193
6-5 The Barrier Potential 199
6-6 Examples of Barrier Penetration by Particles 205
6-7 The Square Well Potential 209
6-8 The Infinite Square Well Potential 214
6-9 The Simple Harmonic Oscillator Potential 221
6-10 Summary 225
7 ONE-ELECTRON ATOMS 232
7-1 Introduction 233
7-2 Development of the Schroedinger Equation 234
7-3 Separation of the Time-Independent Equation 235
7-4 Solution of the Equations 237
7-5 Eigenvalues, Quantum Numbers, and Degeneracy 239
7-6 Eigenfunctions 242
7-7 Probability Densities 244
7-8 Orbital Angular Momentum 254
7-9 Eigenvalue Equations 259
8 MAGNETIC DIPOLE MOMENTS, SPIN, AND TRANSITION RATES 266
8-1 Introduction 267
8-2 Orbital Magnetic Dipole Moments 267
8-3 The Stern-Gerlach Experiment and Electron Spin 272
8-4 The Spin-Orbit Interaction 278
8-5 Total Angular Momentum 281
8-6 Spin-Orbit Interaction Energy and the Hydrogen Energy Levels 284
8-7 Transition Rates and Selection Rules 288
8-8 A Comparison of the Modern and Old Quantum Theories 295
9 MULTIELECTRON ATOMS—GROUND STATES AND
X-RAY EXCITATIONS 300
9-1 Introduction 301
9-2 Identical Particles 302
9-3 The Exclusion Principle 308
9-4 Exchange Forces and the Helium Atom 310
9-5 The Hartree Theory 319 9-6 Results of the Hartree Theory x 322
9-7 Ground States of Multielectron Atoms and the Periodic Table 331
9-8 X-Ray Line Spectra 337
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10 MULTIELECTRON ATOMS—OPTICAL EXCITATIONS 347
10-1 Introduction 348
10-2 Alkali Atoms 349
10-3 Atoms with Several Optically Active Electrons 352
10-4 LS Coupling 356
10-5 Energy Levels of the Carbon Atom 361
10-6 The Zeeman Effect 364
10-7 Summary 370
11 QUANTUM STATISTICS 375
11-1 Introduction 376
11-2 Indistinguishability and Quantum Statistics 377
11-3 The Quantum Distribution Functions 380
11-4 Comparison of the Distribution Functions 384
11-5 The Specific Heat of a Crystalline Solid 388
11-6 The Boltzmann Distributions as an Approximation to Quantum
Distributions 391
11-7 The Laser 392
11-8 The Photon Gas 398
11-9 The Phonon Gas 399
11-10 Bose Condensation and Liquid Helium 399
11-11 The Free Electron Gas 404
11-12 Contact Potential and Thermionic Emission 407
11-13 Classical and Quantum Descriptions of the State of a System 409
12 MOLECULES 415
12-1 Introduction 416
12-2 Ionic Bonds 416
12-3 Covalent Bonds 418
12-4 Molecular Spectra 422
12-5 Rotational Spectra 423
12-6 Vibration-Rotation Spectra 426
12-7 Electronic Spectra 429
12-8 The Raman Effect 432
12-9 Determination of Nuclear Spin and Symmetry Character 434
13 SOLIDS—CONDUCTORS AND SEMICONDUCTORS 442
13-1 Introduction 443
13-2 Types of Solids 443
13-3 Band Theory of Solids 445
13-4 Electrical Conduction in Metals 450
13-5 The Quantum Free-Electron Model 452
13-6 The Motion of Electrons in a Periodic Lattice 456
13-7 Effective Mass 460
13-8 Electron-Positron Annihilation in Solids 464
13-9 Semiconductors 467
13-10 Semiconductor Devices 472 CONTENTS
14 SOLIDS—SUPERCONDUCTORS AND MAGNETIC PROPERTIES 483
14-1 Superconductivity 484
14-2 Magnetic Properties of Solids 492
14-3 Paramagnetism 493
14-4 Ferromagnetism 497
14-5 Antiferromagnetism and Ferrimagnetism 503
15 NUCLEAR MODELS 508
15-1 Introduction 509
15-2 A Survey of Some Nuclear Properties 510
15-3 Nuclear Sizes and Densities 515
15-4 Nuclear Masses and Abundances 519
15-5 The Liquid Drop Model 526
15-6 Magic Numbers 530
15-7 The Fermi Gas Model 531
15-8 The Shell Model 534
15-9 Predictions of the Shell Model 540
15-10 The Collective Model 545
15-11 Summary 549
16 NUCLEAR DECAY AND NUCLEAR REACTIONS 554
16-1 Introduction 555
16-2 Alpha Decay 555
16-3 Beta Decay 562
16-4 The Beta-Decay Interaction 572
16-5 Gamma Decay 578
16-6 The Mössbauer Effect 584
16-7 Nuclear Reactions 588
16-8 Excited States of Nuclei 598
16-9 Fission and Reactors 602
16-10 Fusion and the Origin of the Elements 607
17 INTRODUCTION TO ELEMENTARY PARTICLES 617
17-1 Introduction 618
17-2 Nucleon Forces 618
17-3 Isospin 631
17-4 Pions 634
17-5 Leptons 641
17-6 Strangeness 643
17-7 Families of Elementary Particles 649
17-8 Observed Interactions and Conservation Laws 653
18 MORE ELEMENTARY PARTICLES 666
18-1 Introduction 667
18-2 Evidence for Partons 667
18-3 Unitary Symmetry and Quarks 673
18-4 Extensions of SU(3)—More Quarks 678
18-5 Color and the Color Interaction 683
18-6 Introduction to Gauge Theories 688
18-7 Quantum Chromodynamics 691
18-8 Electroweak Theory 699
18-9 Grand Unification and the Fundamental Interactions 706 Appendix A The Special Theory of Relativity
Appendix B Radiation from an Accelerated Charge
Appendix C The Boltzmann Distribution
Appendix D Fourier Integral Description of a Wave Group
Appendix E Rutherford Scattering Trajectories
Appendix F Complex Quantities
Appendix G Numerical Solution of the Time-Independent Schroedinger
Equation for a Square Well Potential
Appendix H Analytical Solution of the Time-Independent Schroedinger
Equation for a Square Well Potential
Appendix I Series Solution of the Time-Independent Schroedinger
Equation for a Simple Harmonic Oscillator Potential
Appendix J Time-Independent Perturbation Theory
Appendix K Time-Dependent Perturbation Theory
Appendix L The Born Approximation
Appendix M The Laplacian and Angular Momentum Operators in
Spherical Polar Coordinates
Appendix N Series Solutions of the Angular and Radial Equations for
a One-Electron Atom
Appendix O The Thomas Precession
Appendix P The Exclusion Principle in LS Coupling
Appendix Q Crystallography
Appendix R Gauge Invariance in Classical and Quantum Mechanical
Electromagnetism
Appendix S Answers to Selected Problems
Index
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